报告题目：Rank-distance codes and determinantal varieties
报告人：段炼  (上海科技大学)
报告时间：6月19日10：30-11：30
报告地点：四川师范大学数学科学学院205
报告摘要： Using ideas from algebraic geometry, we give a short proof of asymptotic sparsity of maximum rank-distance (MRD) codes over finite fields. More generally, we show that the density of [m, n, k; \delta] codes within the relevant Grassmannian tends to 0 as q\to \infty, provided that (\delta-1)(m+n-\delta+1)\geq mn-k+2 and tends to 1 as q\to \infty, provided that (\delta-1)(m+n-\delta+1)\leq mn-k. These results were proved by Gruica and Ravagnani using a delicate combinatorial argument. Our new method also leads to an explicit formula for the missing case (\delta-1)(m+n-\delta+1)= mn-k+1, where the density tends to 1/e for large m and n. This latter result was previously established by Antrobus and Gluesing-Luerssen for the special case when n=\delta=2 and m=k. 
报告人简介：段炼，上海科技大学数学科学研究所助理教授。2019年博士毕业于马萨诸塞州立大学阿默斯特分校。研究方向包括数论，伽罗华表示理论以及有限域上的代数几何。在Journal of Number Theory，Mathematische Zeitschrift, Nagoya Mathematical Journal, Mathematical Research Letters, Mathematics of Computation等杂志发表论文。

编辑：王苗   审核：舒乾宇   终审：屈加文